Problem: What do the following two equations represent? $5x+2y = -4$ $-6x+15y = 3$
Answer: Putting the first equation in $y = mx + b$ form gives: $5x+2y = -4$ $2y = -5x-4$ $y = -\dfrac{5}{2}x - 2$ Putting the second equation in $y = mx + b$ form gives: $-6x+15y = 3$ $15y = 6x+3$ $y = \dfrac{2}{5}x + \dfrac{1}{5}$ The slopes are negative inverses of each other, so the lines are perpendicular.